Combine 360 HDR with video background
On a side note, I would use the Background BSDF for the worlds background.

You can use the Texture Coordinates Window socket (which you are using already) to determine, wether a light ray is inside the cameras view or outside.



Separate the Window sockets output into its channels. This will result in X, Y and Z coordinates from the camera view window. We are interested in the X and Y values which are inbetween of [0, 1]. We can filter them out with the Greater than and Less than nodes.